Can you draw the next shape in the pattern. How many squares will it have?
Now, without drawing the shapes, can you figure out how many squares will be in the 5th shape? the 10th shape? the 100th shape?
How about the “nth” shape?
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The next shape (the 4th will have 17 squares. The 5th will have 26. The 10th will have 101. The 100th shape will have 10,001 squares. The nth shape will have n2 + 1 squares.
This problem comes from Conceptual Algebra Readiness for Everyone.